Whether or not batteries get lighter as they lose energy is a question that has vexed Yahoo Answers since amateur physicists first found the internet. So to settle the question, YouTuber Tom Scott tracked down half a dozen renowned professors (and a Tesla Model S). Their answer? A dead battery is lighter than a charged one, but on a microscopic scale.
As Scott explains, the mass lost is equivalent to the battery’s energy, divided by the speed of light squared (we know this thanks to e=mc^2). Anything divided by the speed of light squared is going to be an unfathomably tiny number — in this case, less than the weight of the rubber burned off the tires.